For example, a sheet processing apparatus such as a mail sorting apparatus comprises a sheet ejection apparatus configured to eject sheets such as postal matters which are processing targets. Much of the sheet processing apparatuses process the sheets ejected by the sheet ejection apparatus while conveying them. However, the sheets having different thicknesses cannot be often conveyed at the same speed, even if a conveying mechanism operates at a constant speed. For example, when the thicknesses of the sheets increase, a conveying speed tends to be slow. If the conveying speed of each sheet is not constant, gaps between preceding and following sheets conveyed in the sheet processing apparatus vary. When the following sheet catches up the preceding sheet, the sheet processing apparatus cannot normally process the sheets, and hence the apparatus discharges both the following sheet and the preceding sheet.